Document Number: WG14 N749/J11 97-112
C9X Revision Proposal
=====================
Title: LIA-1 Binding:
Author: Fred J. Tydeman
Author Affiliation: Tydeman Consulting
Postal Address: 3711 Del Robles Dr., Austin, Texas, USA, 78727
E-mail Address: tydeman@tybor.com
Telephone Number: +1 (512) 255-8696
Fax Number: +1 (512) 255-8696
Sponsor: WG14
Date: 1997-09-21
Proposal Category:
__ Editorial change/non-normative contribution
__ Correction
Y_ New feature
__ Addition to obsolescent feature list
__ Addition to Future Directions
__ Other (please specify) ______________________________
Area of Standard Affected:
__ Environment
__ Language
__ Preprocessor
Y_ Library
Y_ Macro/typedef/tag name
Y_ Function
Y_ Header
__ Other (please specify) ______________________________
Prior Art: None known.
Target Audience: Programmers writing programs that perform a
significant amount of numeric processing.___________________
Related Documents (if any):
WG14/N758 C9X and LIA-1 informative annex.
WG14/N756 LIA-1 Binding: Arithmetic exception => SIGFPE,
WG14/N755 LIA-1 Binding: to ,
WG14/N753 LIA-1 Binding: Rationale,
WG14/N752 LIA-1 Binding: Optional parts annex,
WG14/N751 LIA-1 Binding: Combined LIA-1 + IEC-559 annex,
WG14/N750 LIA-1 Binding: LIA-1 annex,
WG14/N748 LIA-1 Binding: Adding 'pole' from LIA-2,
WG14/N747 IEC 559 Binding: Signaling NaNs,
WG14/N693 Type-Generic Math Functions,
WG14/N528 C Binding for LIA-1,
WG14/N488 LIA-2 (math library),
WG14/N487 LIA-1 (arithmetic),
WG14/N486 LIA Overview,
WG14/N463 Impact of adding LIA-1,
WG14/N461 C Binding of LIA-1
Proposal Attached: _Y Yes __ No, but what's your interest?
Abstract: These changes are the fundamental changes to C to
allow support of ISO 10967-1 (LIA-1). They are being added
in their own header
Proposal:
Note: The '*' characters in the lefthand column are not part
of the proposal (they are useful for emacs M-x outline mode)
In the following, bold text, italic text,
code sample are the conventions used to indicate
text different from normal.
* -- Add to 6.8.6 Pragma directive:
#pragma STDC LIA_NOTIFY { UNDEF | IGNORE | FLAGS | TRAP }
and add to the list of forward references:
the LIA_NOTIFY pragma (7.x.4.1.1)
* -- Add a new library section (here called 7.x)
** 7.x Notification and additional utilities .
The header declares several macros and functions
to support Language Independent Arithmetic. These are
additional limits (characteristics of the integer and
floating-point types), general integer utilities,
mathematical functions, notification and access to the
integer environment. The integer environment refers
collectively to any integer status flags and control modes
supported by the implementation[footnote]. An integer
status flag is a system variable whose value is set as a
side effect of the arithmetic to provide auxiliary
information. An integer control mode is a system
variable whose value may be set by the user to affect the
subsequent behavior of the arithmetic.
[footnote]. This header is designed to support the
notification indicators (here called exception status flags)
required by LIA-1, and other similar integer state
information. Also it is designed to facilitate code
portability among all systems.
*** 7.x.1 Limits
Several macros are declared to provide additional
information beyond and
about the characteristics of the integer and floating-point
types.
All integral values in the header, shall be
constant expressions suitable for use in #if preprocessing
directives; all floating values shall be constant
expressions. Most floating-point related macros have
separate names for all three floating-point types.
**** 7.x.1.1 Integer limits
The treatment of out-of-bounds results
0 undefined behavior
1 wrap (similar to unsigned)
2 notification
for the signed integer types int, long and
long long are characterized by
INT_OUT_OF_BOUNDS
**** 7.x.1.2 Floating-point limits
The values given in the following list shall be replaced by
implementation-defined expressions that shall be equal or
lesser in magnitude (absolute value) to those shown, with
the same sign:
-- maximum rounding error of, at least the operations,
+, -, *, and /, in terms of Units in Last Place (ULPs),
for each floating-point type,
FLT_RND_ERR 7.0
In general, for normal results, the rounding error, re, is
defined by:
| tr - cr | <= re * ulp(cr)
where
tr = infinitely precise true result
cr = computed result
For the full details, including difference between normals
and subnormals, see LIA-1 subclause 5.2.8 Rounding
constants.
The values given in the following list shall be replaced by
implementation-defined expressions that shall be equal or
greater in magnitude (absolute value) to those shown, with
the same sign:
-- minimum positive floating-point number, b**emin-p if
subnormalized numbers are supported, else b**emin-1,
FLT_TRUE_MIN 1E-37
DBL_TRUE_MIN 1E-37
LDBL_TRUE_MIN 1E-37
The level of support for subnormalized numbers is
characterized by the values
-1 indeterminable
0 not supported
1 fully supported
2 treated as zero
for the floating types float, double, long double
FLT_SUBNORMALDBL_SUBNORMALLDBL_SUBNORMAL
respectively.
All other negative values for *_SUBNORMAL
characterize implementation-defined behavior.
The values given in the following list shall be replaced by
implementation-defined expressions:
-- boolean value (0 or 1) to indicate if the corresponding
type conforms to IEC 559,
FLT_IEC_559DBL_IEC_559LDBL_IEC_559
Example 2 in is supplemented with these:
FLT_RND_ERR 0.5
FLT_IEC_559 1
FLT_SUBNORMAL 1
FLT_TRUE_MIN 1.40129846E-45
DBL_IEC_559 1
DBL_SUBNORMAL 1
DBL_TRUE_MIN 4.94065646E-324
*** 7.x.2 Mathematics
Several functions are declared to provide additional
capability beyond . Most synopses specify a
function which takes one or more double arguments and
returns a double value; for each such function, there
are functions with the same name but with f and
l suffixes which are corresponding functions with
float and long double arguments and return
values.
**** 7.x.2.1 Exponential and logarithmic functions
***** 7.x.2.1.1 The fracrep functionSynopsis#include double fracrep(double x);Description
The fracrep function extracts the fraction of the
model representation of x, as a signed normalized
fraction in the format of x.
Returns
The fracrep function returns the value y, such
that y is a double with magnitude in the
interval [1/FLT_RADIX, 1) or zero, and x equals
y times FLT_RADIX raised to the power
(logb(x)+1.0). The value returned for zero is 0.0.
***** 7.x.2.1.2 The ulp functionSynopsis#include double ulp(double x);Description
The ulp function computes the value of a Unit in the
Last Place of x. A domain error occurs if the
argument is zero. A range error occurs if the magnitude of
x is too small and subnormals are not supported.
Returns
The ulp function returns the value FLT_RADIX
raised to the power (logb(x)+1-p). p
is the precision of the floating type and is one of
*_MANT_DIG.
**** 7.x.2.2 Sign function
***** 7.x.2.2.1 The fsgn functionSynopsis#include double fsgn(double x);Description
The fsgn function computes the sign of a
floating-point number x. Positive floating-point
numbers have a sign of +1.0, negative floating-point numbers
have a sign of -1.0, and zero has a sign of 0.0.
Returns
The fsgn function returns the sign.
**** 7.x.2.3 Manipulation functions
***** 7.x.2.3.1 The fsucc functionSynopsis#include double fsucc(double x);Description
The fsucc function determines the next representable
value, in the type of the function, after x in the
direction of +infinity. A range error occurs if x is
the largest positive finite number.
Returns
The fsucc function returns the smallest representable
value, of the same type, greater than x.
***** 7.x.2.3.2 The fpred functionSynopsis#include double fpred(double x);Description
The fpred function determines the next representable
value, in the type of the function, after x in the
direction of -infinity. A range error occurs if x is
the largest negative finite number.
Returns
The fpred function returns the largest representable
value, of the same type, less than x.
***** 7.x.2.3.3 The truncto functionSynopsis#include double truncto(double x, int n);Description
The truncto function truncates (rounds toward zero)
x to n digits of precision.
Returns
The truncto function returns the value for normal
numbers: sign(x) * floor(|x|/(FLT_RADIX**(expon(x)-n))) *
FLT_RADIX**(expon(x)-n) and for subnormal numbers: sign(x) *
floor(|x|/(FLT_RADIX**(emin-n))) * FLT_RADIX**(emin-n). If
n is less than 1, returns 0. If n is greater
than precision of x, returns x.
***** 7.x.2.3.4 The roundto functionSynopsis#include double roundto(double x, int n);Description
The roundto function rounds (rounds to biased nearest
with ties going away from zero) x to n digits
of precision. A range error may occur.
Returns
The roundto function returns the value for normal
numbers: sign(x) * floor(|x|/(FLT_RADIX**(expon(x)-n))+0.5)
* FLT_RADIX**(expon(x)-n) and for subnormal numbers: sign(x)
* floor(|x|/(FLT_RADIX**(emin-n))+0.5) * FLT_RADIX**(emin-n).
If n is less than 1, returns 0. If n is
greater than precision of x, returns x.
**** 7.x.2.4 Conversion macros
The following subclauses provide macros that convert from
floating-point type to integral type using round to nearest
rounding. The round to nearest can be biased (ties round
away from zero) or unbiased (such as IEC 559 round to
nearest even). In the synopses in this subclause,
real-floating indicates that the argument must be an
expression of real floating type.
***** 7.x.2.4.1 The icvt macroSynopsis#include int icvt(real-floating x);Description
The icvt macro rounds its argument to the nearest
integral value. If the rounded value is outside the range
of int, the numeric result is unspecified. A
range error may occur if the magnitude of x
is too large.
Returns
The icvt macro returns the rounded integral value.
***** 7.x.2.4.2 The lcvt macroSynopsis#include long lcvt(real-floating x);Description
The lcvt macro is equivalent to the icvt
macro, except that the returned value has type long.
***** 7.x.2.4.3 The llcvt macroSynopsis#include long long llcvt(real-floating x);Description
The llcvt macro is equivalent to the icvt
macro, except that the returned value has type long
long.
***** 7.x.2.4.4 The uicvt macroSynopsis#include unsigned int uicvt(real-floating x);Description
The uicvt macro rounds its argument to the nearest
integral value. If the rounded value is outside the range
of unsigned int, the rounded value is wrapped modulo
(UINT_MAX+1).
Returns
The uicvt macro returns the rounded integral value.
***** 7.x.2.4.5 The ulcvt macroSynopsis#include unsigned long ulcvt(real-floating x);Description
The ulcvt macro is equivalent to the uicvt
macro, except that the returned value has type unsigned
long.
***** 7.x.2.4.6 The ullcvt macroSynopsis#include unsigned long long ullcvt(real-floating x);Description
The ullcvt macro is equivalent to the uicvt
macro, except that the returned value has type unsigned
long long.
*** 7.x.3 General utilities
Several functions are declared to provide additional
capability beyond .
**** 7.x.3.1 The sgn functionSynopsis#include int sgn(int j);Description
The sgn function computes the sign of an integer
j. Positive integers have a sign of +1, negative
integers have a sign of -1, and zero has a sign of 0.
Returns
The sgn function returns the sign.
**** 7.x.3.2 The lsgn functionSynopsis#include long int lsgn(long int j);Description
The lsgn function is similar to the sgn
function, except that the argument and returned value each
have type long int.
**** 7.x.3.3 The llsgn functionSynopsis#include long long int llsgn(long long int j);Description
The llsgn function is similar to the sgn
function, except that the argument and returned value each
have type long long int.
**** 7.x.3.4 The modulo functionSynopsis#include int modulo(int numer, int denom);Description
The modulo function computes the modulus, that is,
[Ed: math equation] numer-(floor(numer/denom)*denom).
If denom is zero, the behavior is undefined.
Returns
The modulo function returns the modulus.
**** 7.x.3.5 The lmodulo functionSynopsis#include long int lmodulo(long int numer, long int denom);Description
The lmodulo function is similar to the modulo
function, except that the arguments and returned value each
have type long int.
**** 7.x.3.6 The llmodulo functionSynopsis#include long long int llmodulo(long long int numer,
long long int denom);Description
The llmodulo function is similar to the modulo
function, except that the arguments and returned value each
have type long long int.
*** 7.x.4 Notification
Each macro
INT_OVERFLOWINT_DIVBYZEROINT_INVALID
is defined if and only if the implementation supports the
exception by means of the functions in 7.x.4.2. The defined
macros expand to integral constant expressions whose values
are distinct powers of 2.
The macro
INT_ALL_EXCEPT
is simply the bitwise OR of all integer exception macros
defined by the implementation.
These next three macros describe what notifications happen
for conversions of values from floating-point types to
integral types for some specific values.
-- value to indicate what notification happens for
NaNs,
FP2INT_OF_NAN
It should be INT_INVALID, but may be FE_INVALID or another
exception indicator macro.
-- value to indicate what notification happens for
infinities,
FP2INT_OF_INF
It should be INT_INVALID, but may be FE_INVALID or another
exception indicator macro.
-- value to indicate what notification happens for
out-of-bounds integral values,
FP2INT_OF_LARGE
It should be INT_OVERFLOW, but may be FE_INVALID or another
exception indicator macro, when INT_OUT_OF_BOUNDS is 2
(notify).
The FP2INT_OF_LARGE macro shall be 0 (meaning no exception)
when INT_OUT_OF_BOUNDS is 1 (wrap).
The macro
DISTINGUISH_INT_DIV_BY_ZERO
has a boolean value (0 or 1) to indicate if 0/0 can be
distinguished from non-zero/zero. If this is true,
then 0/0 will notify as invalid, else, as divbyzero.
The macro
DISTINGUISH_FP_DIV_BY_ZERO
has a boolean value (0 or 1) to indicate if 0.0/0.0 can be
distinguished from finite non-zero/zero. If this is true,
then 0.0/0.0 will notify as invalid, else, as divbyzero.
**** 7.x.4.1 The LIA_NOTIFY pragma and macro
***** 7.x.4.1.1 The LIA_NOTIFY pragmaSynopsis#include #pragma STDC LIA_NOTIFY { UNDEF | IGNORE | FLAGS | TRAP }Description
The LIA_NOTIFY pragma provides a means to inform the
implementation which notification mechanism is to be
used[footnote]. The pragma can occur either outside
external declarations or preceding all explicit declarations
and statements inside a compound statement. When outside
external declarations, the pragma takes effect from its
occurrence until another LIA_NOTIFY pragma is encountered,
or until the end of the translation unit. When inside a
compound statement, the pragma takes effect from its
occurrence until another LIA_NOTIFY pragma is encountered
(within a nested compound statement), or until the end of
the compound statement; at the end of a compound statement
the state for the pragma is restored to its condition just
before the compound statement. The effect of this pragma in
any other context is undefined. If part of a program tests
flags or runs under non-default mode settings, but was
translated with the state for the LIA_NOTIFY pragma UNDEF,
then the behavior of that program is undefined.
UNDEF shall cause notifications to be undefined behaviour.
This matches C89/C95.
IGNORE shall cause notifications to be ignored. Traps shall
not be taken. It is implementation defined if status flags
will be set. An implementation defined continuation value
will be used in place of the failing arithmetic operation.
This causes the final check of the status flags at program
termination to be suppressed. This allows the optimizations
mentioned in the subsection on "FENV_ACCESS off" to be done.
FLAGS shall cause notifications to set a status flag and
proceed with a continuation value in place of the arithmetic
failure. It is implementation defined if the final check of
some status flags at program termination will be performed.
TRAP shall cause notifications to trap. It is
implementation defined if a trap shall be turned into a
raise of some signal, or result in program termination.
Until is included, the default state for the
pragma shall be UNDEF. Once is included, the
default state for the pragma is implementation-defined and
shall be one of FLAGS, TRAP, (or DYNAMIC if supported).
It is implementation defined if the different translation
units that comprise a program are translated with different
LIA_NOTIFY states.
It is implementation defined which of INT_OVERFLOW,
INT_DIVBYZERO, INT_INVALID, FE_INEXACT,
FE_UNDERFLOW, FE_OVERFLOW,
FE_DIVBYZERO, and FE_INVALID are defined.
Those defined determine the set of notifications being
checked.
[footnote]Notification is the process by which a program is
informed that an arithmetic operation cannot be performed.
***** 7.x.4.1.2 The LIA_NOTIFY macro
The macro
LIA_NOTIFY
has one of these values (with corresponding meaning)
0 Undefined, like C89/C95
1 Notifications are ignored
2 All notifications will set flags
3 All notifications will trap
4 Program switches between flags and traps at runtime
to indicate the current way notifications are being handled.
That is, the macro tracks the state of the LIA_NOTIFY
pragma.
**** 7.x.4.2 Exception flags
The following functions provide access to the integer
exception flags. They support the basic abstraction of
flags that are either set or clear. The int input
argument for the functions represents a subset of integer
exceptions, and can be constructed by bitwise ORs of the
integer exception macros, for example (INT_DIVBYZERO |
INT_INVALID). For other argument values the behavior of
these functions is undefined.
***** 7.x.4.2.1 The ieclearexcept functionSynopsis#include void ieclearexcept(int excepts);Description
The ieclearexcept function clears the supported integer
exceptions represented by its argument.
***** 7.x.4.2.2 The ieraiseexcept functionSynopsis#include void ieraiseexcept(int excepts);Description
The ieraiseexcept function raises the supported integer
exceptions represented by its argument. The order in which
these exceptions are raised is unspecified.
***** 7.x.4.2.3 The ietestexcept functionSynopsis#include int ietestexcept(int excepts);Description
The ietestexcept function determines which of a specified
subset of the integer exception flags are currently set.
The excepts argument specifies the integer exception
flags to be queried.[footnote]
[footnote]. This mechanism allows testing several
exceptions with just one function call.
Returns
The ietestexcept function returns the value of the bitwise
OR of the integer exception macros corresponding to the
currently set exceptions included in excepts.
* -- Add to 7.? Type-generic math :
after all occurances of
** -- Add to 7.?.1 Type-generic macros
*** -- Add to the list of real (but not complex) functions that
starts atan2, exp2:
fracrepulpfsgnfsuccfpredtrunctoroundto
* -- Add to Annex D Library summary
** -- Add new subclause: D.x Notification and additional utilities
*** -- Add new subclause: D.x.1 Limits
**** -- Add new subclause: D.x.1.1 Integral limitsINT_OUT_OF_BOUNDS
**** -- Add new subclause: D.x.1.2 Floating-point limitsFLT_RND_ERRFLT_TRUE_MINDBL_TRUE_MINLDBL_TRUE_MINFLT_SUBNORMALDBL_SUBNORMALLDBL_SUBNORMALFLT_IEC_559DBL_IEC_559LDBL_IEC_559
*** -- Add new subclause: D.x.2 Mathematics
[Note to editor: If we need to include the float and long
double versions, here, and in and ,
please add them.]
double fracrep(double x);double ulp(double x);double fsgn(double x);double fsucc(double x);double fpred(double x);double truncto(double x, int n);double roundto(double x, int n);
*** -- Add new subclause: D.x.3 General utilitiesint icvt(real-floating x);long lcvt(real-floating x);long long llcvt(real-floating x);unsigned int uicvt(real-floating x);unsigned long ulcvt(real-floating x);unsigned long long ullcvt(real-floating x);int sgn(int j);long int lsgn(long int j);long long int llsgn(long long int j);int modulo(int numer, int denom);long int lmodulo(long int numer, long int denom);long long int llmodulo(long long int numer,
long long int denom);
*** -- Add new subclause: D.x.4 NotificationINT_OVERFLOWINT_DIVBYZEROINT_INVALIDINT_ALL_EXCEPTFP2INT_OF_NANFP2INT_OF_INFFP2INT_OF_LARGEDISTINGUISH_INT_DIV_BY_ZERODISTINGUISH_FP_DIV_BY_ZERO#pragma STDC LIA_NOTIFY { UNDEF | IGNORE | FLAGS | TRAP }LIA_NOTIFYvoid ieclearexcept(int excepts);void ieraiseexcept(int excepts);int ietestexcept(int excepts);
* -- Add to Annex F IEC 559 Floating-Point Arithmetic:
** -- Add new subclause F.10 :
*** F.10.1 Exponential and logarithmic functions
**** F.10.1.1 The fracrep function
fracrep(-0.0) returns -0.0
fracrep(+/-INFINITY) returns +/-INFINITY
**** F.10.1.2 The ulp function
ulp(-0.0) returns a NaN and raises the invalid
exception.
ulp(+/-INFINITY) returns a NaN and raises the invalid
exception.
ulp(1.0) returns DBL_EPSILON.
*** F.10.2 Sign function
**** F.10.2.1 The fsgn function
fsgn(-0.0) returns -0.0
fsgn(+INFINITY) returns +1.0
fsgn(-INFINITY) returns -1.0
fsgn(NaN) returns the same NaN.
*** F.10.3 Manipulation functions
**** F.10.3.1 The fsucc function
fsucc(-0.0) returns +DBL_TRUE_MIN
fsucc(+INFINITY) returns +INFINITY
fsucc(+DBL_MAX) returns +INFINITY and raises overflow.
**** F.10.3.2 The fpred function
fpred(-0.0) returns -DBL_TRUE_MIN
fpred(-INFINITY) returns -INFINITY
fpred(-DBL_MAX) returns -INFINITY and raises overflow.
**** F.10.3.3 The truncto function
truncto(-0.0, n) returns -0.0 for any n.
truncto(+/-INFINITY, n) returns +/-INFINITY for any n.
truncto(NaN, n) returns the same NaN for any n.
**** F.10.3.4 The roundto function
roundto(-0.0, n) returns -0.0 for any n.
roundto(+/-INFINITY, n) returns +/-INFINITY for any n.
roundto(NaN, n) returns the same NaN for any n.
*** F.10.4 Conversion macros
**** F.10.4.1 The icvt macro
icvt(NaN) returns an unspecified value and raises
FP2INT_OF_NAN.
icvt(+/-INFINITY) returns an unspecified value and
raises FP2INT_OF_INF.
**** F.10.4.2 The lcvt macro
lcvt(NaN) returns an unspecified value and raises
FP2INT_OF_NAN.
lcvt(+/-INFINITY) returns an unspecified value and
raises FP2INT_OF_INF.
**** F.10.4.3 The llcvt macro
llcvt(NaN) returns an unspecified value and raises
FP2INT_OF_NAN.
llcvt(+/-INFINITY) returns an unspecified value and
raises FP2INT_OF_INF.
**** F.10.4.4 The uicvt macro
uicvt(NaN) returns an unspecified value and raises
FP2INT_OF_NAN.
uicvt(+/-INFINITY) returns an unspecified value and
raises FP2INT_OF_INF.
**** F.10.4.5 The ulcvt macro
ulcvt(NaN) returns an unspecified value and raises
FP2INT_OF_NAN.
ulcvt(+/-INFINITY) returns an unspecified value and
raises FP2INT_OF_INF.
**** F.10.4.6 The ullcvt macro
ullcvt(NaN) returns an unspecified value and raises
FP2INT_OF_NAN.
ullcvt(+/-INFINITY) returns an unspecified value and
raises FP2INT_OF_INF.